On the shape of compact hypersurfaces with almost constant mean curvature
Analysis of PDEs
2015-04-13 v2 Differential Geometry
Metric Geometry
Abstract
The distance of an almost constant mean curvature boundary from a finite family of disjoint tangent balls with equal radii is quantitatively controlled in terms of the oscillation of the scalar mean curvature. This result allows one to quantitatively describe the geometry of volume-constrained stationary sets in capillarity problems.
Keywords
Cite
@article{arxiv.1503.06674,
title = {On the shape of compact hypersurfaces with almost constant mean curvature},
author = {Giulio Ciraolo and Francesco Maggi},
journal= {arXiv preprint arXiv:1503.06674},
year = {2015}
}
Comments
36 pages, 2 figures. In this version we have added an appendix about almost umbilical surfaces